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A hierarchy (from the Greek ἱεραρχία hierarkhia, "rule of a high priest", from hierarkhes, "president of sacred rites") is an arrangement of items (objects, names, values, categories, etc.) in which the items are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important concept in a wide variety of fields, such as philosophy, mathematics, computer science, organizational theory, systems theory, and the social sciences (especially political philosophy).

A hierarchy (from the Greek ἱεραρχία hierarkhia, "rule of a high priest", from hierarkhes, "president of sacred rites") is an arrangement of items (objects, names, values, categories, etc.) in which the items are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important concept in a wide variety of fields, such as philosophy, mathematics, computer science, organizational theory, systems theory, and the social sciences (especially political philosophy).

层级(来自希腊的大祭司的统治，来自大祭司的统治，来自于大祭司的统治，来自于神圣仪式的总统)是一种项目的安排(对象，名字，价值观，类别等等)其中项目表示为“上面”、“下面”或“与其他项目处于同一水平”。等级是一个重要的概念，在各种各样的领域，如哲学，数学，计算机科学，组织行为学，系统理论，和社会科学(特别是政治哲学)。

层级(来自希腊的大祭司的统治，来自大祭司的统治，来自于大祭司的统治，来自于神圣仪式的总统)是一种项目的安排(对象，名字，价值观，类别等等)其中项目表示为“上面”、“下面”或“与其他项目处于同一水平”。等级是一个重要的概念，在各种各样的领域，如哲学，数学，计算机科学，组织行为学，系统理论，和社会科学(特别是政治哲学)。

层次结构可以直接或间接地连接实体，也可以垂直或对角地连接。层次结构中唯一的直接联系，只要它们是等级的，就是与一个人的直接上级或者与一个人的下级的直接联系，尽管一个主要是等级结构的系统也可以包含替代的等级结构。层次链接可以延伸“垂直”向上或向下通过多个链接在同一方向，遵循一个路径。层次结构中没有垂直相连的所有部分都可以通过一条路径“水平”相连，即沿着层次结构向上走，找到一个共同的直接或间接的上级，然后再向下。这类似于两个同事或同事; 每个人向一个共同的上级汇报，但他们拥有相同的相对权限。组织形式的存在是层次结构的替代和补充。异质结构就是这样一种形式。

层次结构可以直接或间接地连接实体，也可以垂直或对角地连接。层次结构中唯一的直接联系，只要它们是等级的，就是与一个人的直接上级或者与一个人的下级的直接联系，尽管一个主要是等级结构的系统也可以包含替代的等级结构。层次链接可以延伸“垂直”向上或向下通过多个链接在同一方向，遵循一个路径。层次结构中没有垂直相连的所有部分都可以通过一条路径“水平”相连，即沿着层次结构向上走，找到一个共同的直接或间接的上级，然后再向下。这类似于两个同事或同事; 每个人向一个共同的上级汇报，但他们拥有相同的相对权限。组织形式的存在是层次结构的替代和补充。异质结构就是这样一种形式。

==Nomenclature==

 

==名称 Nomenclature==

{{see also| Glossary of graph theory| Taxonomy (general)| Structure}}

{{see also| Glossary of graph theory| Taxonomy (general)| Structure}}

===Degree of branching <span id="Terminology"></span>===

===支化度 Degree of branching <span id="Terminology"></span>===

[[Degree (graph theory)|Degree]] of [[Bifurcation theory|branching]] refers to the number of direct [[#Terminology|subordinates]] or children an object has (in graph theory, equivalent to the number of other [[vertex (graph theory)|vertices]] connected to via outgoing arcs, in a directed graph) a node has. Hierarchies can be categorized based on the "maximum degree", the highest degree present in the system as a whole. Categorization in this way yields two broad classes: ''linear'' and ''branching''.

[[Degree (graph theory)|Degree]] of [[Bifurcation theory|branching]] refers to the number of direct [[#Terminology|subordinates]] or children an object has (in graph theory, equivalent to the number of other [[vertex (graph theory)|vertices]] connected to via outgoing arcs, in a directed graph) a node has. Hierarchies can be categorized based on the "maximum degree", the highest degree present in the system as a whole. Categorization in this way yields two broad classes: ''linear'' and ''branching''.

==History of the term==

==术语历史 History of the term==

Possibly the first use of the English word "hierarchy" cited by the ''[[Oxford English Dictionary]]'' was in 1881, when it was used in reference to the three orders of three angels as depicted by [[Pseudo-Dionysius the Areopagite]] (5th–6th centuries). Pseudo-Dionysius used the related [[Ancient Greek|Greek]] word (ἱεραρχία ''hierarchia'') both in reference to the [[De Coelesti Hierarchia|celestial hierarchy]] and the [[ecclesiastical hierarchy]].<ref>[http://www.newadvent.org/cathen/07322c.htm CATHOLIC ENCYCLOPEDIA: Hierarchy<!-- Bot generated title -->]</ref> The Greek term ἱεραρχία means "rule of a high priest"<ref>[https://www.etymonline.com/word/hierarchy "hierarchy"]. [[Online Etymology Dictionary]].</ref> (from ἱεράρχης ''hierarches'', meaning "president of sacred rites, high-priest"<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Di%28era%2Frxhs ἱεράρχης],

Possibly the first use of the English word "hierarchy" cited by the ''[[Oxford English Dictionary]]'' was in 1881, when it was used in reference to the three orders of three angels as depicted by [[Pseudo-Dionysius the Areopagite]] (5th–6th centuries). Pseudo-Dionysius used the related [[Ancient Greek|Greek]] word (ἱεραρχία ''hierarchia'') both in reference to the [[De Coelesti Hierarchia|celestial hierarchy]] and the [[ecclesiastical hierarchy]].<ref>[http://www.newadvent.org/cathen/07322c.htm CATHOLIC ENCYCLOPEDIA: Hierarchy<!-- Bot generated title -->]</ref> The Greek term ἱεραρχία means "rule of a high priest"<ref>[https://www.etymonline.com/word/hierarchy "hierarchy"]. [[Online Etymology Dictionary]].</ref> (from ἱεράρχης ''hierarches'', meaning "president of sacred rites, high-priest"<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Di%28era%2Frxhs ἱεράρχης],

==Visual hierarchy==

==视觉层次 Visual hierarchy==

In the design field, mainly graphic design, successful layouts and formatting of the content on documents are heavily dependent on the rules of [[visual hierarchy]]. Visual hierarchy is also important for proper organization of files on computers.

In the design field, mainly graphic design, successful layouts and formatting of the content on documents are heavily dependent on the rules of [[visual hierarchy]]. Visual hierarchy is also important for proper organization of files on computers.

==Informal representation==

==通俗表达 Informal representation==

In plain English, a hierarchy can be thought of as a [[Set (mathematics)|set]] in which:<ref name="Dawkins">{{cite conference|last=Dawkins|first=Richard|authorlink=Richard Dawkins|title=Hierarchical organization: a candidate principle for ethology|conference=Growing points in ethology: based on a conference sponsored by St. John's College and King's College, Cambridge|editor1=Bateson, Paul Patrick Gordon |editor2=Hinde, Robert A.|year=1976|publisher=Cambridge University Press|location=Cambridge, England|isbn=0-521-29086-4|pages=7–54}}</ref>

In plain English, a hierarchy can be thought of as a [[Set (mathematics)|set]] in which:<ref name="Dawkins">{{cite conference|last=Dawkins|first=Richard|authorlink=Richard Dawkins|title=Hierarchical organization: a candidate principle for ethology|conference=Growing points in ethology: based on a conference sponsored by St. John's College and King's College, Cambridge|editor1=Bateson, Paul Patrick Gordon |editor2=Hinde, Robert A.|year=1976|publisher=Cambridge University Press|location=Cambridge, England|isbn=0-521-29086-4|pages=7–54}}</ref>

==Mathematical representation==

==数学表达 Mathematical representation==

{{Main|Hierarchy (mathematics)}}

{{Main|Hierarchy (mathematics)}}

Mathematically, in its most general form, a hierarchy is a partially ordered set or poset.<ref name="Lehmann">{{cite conference|last=Lehmann|first=Fritz|title=Big Posets of Participatings and Thematic Roles|pages=50–74|conference=Conceptual structures: knowledge representation as interlingua—4th International Conference on Conceptual Structures, ICCS '96, Sydney, Australia, August 19–22, 1996—proceedings

Mathematically, in its most general form, a hierarchy is a partially ordered set or poset.<ref name="Lehmann">{{cite conference|last=Lehmann|first=Fritz|title=Big Posets of Participatings and Thematic Roles|pages=50–74|conference=Conceptual structures: knowledge representation as interlingua—4th International Conference on Conceptual Structures, ICCS '96, Sydney, Australia, August 19–22, 1996—proceedings

在数学上，从最一般的形式来看，层次结构是一个偏序集或偏序集。1996年8月19日至22日，在澳大利亚悉尼举行的第四届国际概念结构会议ー会议录

在数学上，从最一般的形式来看，层次结构是一个偏序集或偏序集。1996年8月19日至22日，在澳大利亚悉尼举行的第四届国际概念结构会议ー会议录

|isbn=3-540-61534-2|year=1996|publisher=Springer|editor-last=Eklund|editor-first=Peter G.|editor2-last=Ellis|editor2-first=Gerard|editor3-last=Mann|editor3-first=Graham|series=Lecture Notes in Artificial Intelligence 115|location=Germany}}</ref> The system in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with the same property value are grouped together, and each of those resulting levels is referred to as a class.

|isbn=3-540-61534-2|year=1996|publisher=Springer|editor-last=Eklund|editor-first=Peter G.|editor2-last=Ellis|editor2-first=Gerard|editor3-last=Mann|editor3-first=Graham|series=Lecture Notes in Artificial Intelligence 115|location=Germany}}</ref> The system in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with the same property value are grouped together, and each of those resulting levels is referred to as a class.

[参考译文]本例中的系统是由元素组成的整个波集。在这个系统中，每个元素都具有一个明确的特性。具有相同属性值的对象组合在一起，每个产生的级别都称为类。

[参考译文]本例中的系统是由元素组成的整个波集。在这个系统中，每个元素都具有一个明确的特性。具有相同属性值的对象组合在一起，每个产生的级别都称为类。

"Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. <!--Mathematically, a hierarchy can be depicted as a combinatorial object.-->

"Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. <!--Mathematically, a hierarchy can be depicted as a combinatorial object.-->

“层次结构”特别用来指按照不断增加的复杂性来组织类的偏序集。< ! ——从数学上讲，等级可以被描述为一个组合对象。 -- >  

“层次结构”特别用来指按照不断增加的复杂性来组织类的偏序集。< ! ——从数学上讲，等级可以被描述为一个组合对象。 -- >  

Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to a problem. The use of parenthesis is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example:

Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to a problem. The use of parenthesis is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example:

诸如加、减、乘、除等运算通常是按照一定的顺序进行的。通常，加法和减法是在乘法和除法已经应用到一个问题之后进行的。圆括号的使用也是层次结构的一种表示，因为它们显示了在下列操作之前要完成的操作。例如:

诸如加、减、乘、除等运算通常是按照一定的顺序进行的。通常，加法和减法是在乘法和除法已经应用到一个问题之后进行的。圆括号的使用也是层次结构的一种表示，因为它们显示了在下列操作之前要完成的操作。例如:

In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parentheses are placed, one will know to do the operations within the parentheses first before continuing on with the problem. These rules are largely dominant in algebraic problems, ones that include several steps to solve. The use of hierarchy in mathematics is beneficial to quickly and efficiently solve a problem without having to go through the process of slowly dissecting the problem. Most of these rules are now known as the proper way into solving certain equations.

In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parentheses are placed, one will know to do the operations within the parentheses first before continuing on with the problem. These rules are largely dominant in algebraic problems, ones that include several steps to solve. The use of hierarchy in mathematics is beneficial to quickly and efficiently solve a problem without having to go through the process of slowly dissecting the problem. Most of these rules are now known as the proper way into solving certain equations.

在这个问题中，根据数学层次规则，一个人通常会先乘以5乘以7。但是当放置括号时，人们会知道在继续处理问题之前先在括号内做操作。这些规则在代数问题中占主导地位，这些问题包括需要解决的几个步骤。在数学中使用层次结构有利于快速有效地解决问题，而不必经历慢慢剖析问题的过程。这些规则中的大多数现在被认为是解决某些方程的正确方法。

在这个问题中，根据数学层次规则，一个人通常会先乘以5乘以7。但是当放置括号时，人们会知道在继续处理问题之前先在括号内做操作。这些规则在代数问题中占主导地位，这些问题包括需要解决的几个步骤。在数学中使用层次结构有利于快速有效地解决问题，而不必经历慢慢剖析问题的过程。这些规则中的大多数现在被认为是解决某些方程的正确方法。

==Subtypes==

==亚型 Subtypes==

===Nested hierarchy===<!--if you change this title, change the wiki links within the article that link to it!-->

===嵌套层次 Nested hierarchy===<!--if you change this title, change the wiki links within the article that link to it!-->

===Nested hierarchy===<!--if you change this title, change the wiki links within the article that link to it!-->

===嵌套层次 Nested hierarchy===<!--if you change this title, change the wiki links within the article that link to it!-->

= = = 嵌套层次结构 = = = = < ! -- 如果您更改此标题，请更改链接到该标题的文章中的 wiki 链接! -- >  

= = = 嵌套层次结构 = = = = < ! -- 如果您更改此标题，请更改链接到该标题的文章中的 wiki 链接! -- >  

[[Matryoshka dolls, also known as nesting dolls or Russian dolls. Each doll is encompassed inside another until the smallest one is reached. This is the concept of nesting. When the concept is applied to sets, the resulting ordering is a nested hierarchy.]]

[[Matryoshka dolls, also known as nesting dolls or Russian dolls. Each doll is encompassed inside another until the smallest one is reached. This is the concept of nesting. When the concept is applied to sets, the resulting ordering is a nested hierarchy.]]

[俄罗斯套娃，又称嵌套娃娃或俄罗斯套娃。每个洋娃娃都被包裹在另一个洋娃娃里面，直到最小的洋娃娃被够到。这就是嵌套的概念。当这个概念应用于集合时，结果排序是一个嵌套的层次结构。]]

[俄罗斯套娃，又称嵌套娃娃或俄罗斯套娃。每个洋娃娃都被包裹在另一个洋娃娃里面，直到最小的洋娃娃被够到。这就是嵌套的概念。当这个概念应用于集合时，结果排序是一个嵌套的层次结构。]]

A nested hierarchy or inclusion hierarchy is a hierarchical ordering of nested sets. The concept of nesting is exemplified in Russian matryoshka dolls. Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll; a generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example:

A nested hierarchy or inclusion hierarchy is a hierarchical ordering of nested sets. The concept of nesting is exemplified in Russian matryoshka dolls. Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll; a generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example:

嵌套层次结构或包含层次结构是嵌套集的层次结构排序。嵌套的概念在俄罗斯套娃中得到了体现。每个娃娃都被另一个娃娃包围着，一直到外面的娃娃。外部的玩偶包含所有的内部玩偶，下一个外部的玩偶包含所有剩余的内部玩偶，等等。表示一个嵌套层次结构，其中每个层次只包含一个对象，也就是说，每个娃娃的大小只有一个; 一个广义的嵌套层次结构允许在层次中有多个对象，但每个对象在每个层次上只有一个父对象。一般概念在下面的例子中得到了证明和数学上的表述:

嵌套层次结构或包含层次结构是嵌套集的层次结构排序。嵌套的概念在俄罗斯套娃中得到了体现。每个娃娃都被另一个娃娃包围着，一直到外面的娃娃。外部的玩偶包含所有的内部玩偶，下一个外部的玩偶包含所有剩余的内部玩偶，等等。表示一个嵌套层次结构，其中每个层次只包含一个对象，也就是说，每个娃娃的大小只有一个; 一个广义的嵌套层次结构允许在层次中有多个对象，但每个对象在每个层次上只有一个父对象。一般概念在下面的例子中得到了证明和数学上的表述:

====Containment hierarchy====

====包容层次 Containment hierarchy====

A containment hierarchy is a direct extrapolation of the [[#Nested hierarchy|nested hierarchy]] concept. All of the ordered sets are still nested, but every set must be "[[strict subset|strict]]"—no two sets can be identical. The shapes example above can be modified to demonstrate this:

A containment hierarchy is a direct extrapolation of the [[#Nested hierarchy|nested hierarchy]] concept. All of the ordered sets are still nested, but every set must be "[[strict subset|strict]]"—no two sets can be identical. The shapes example above can be modified to demonstrate this:

=====Subsumptive containment hierarchy=====

=====包含的包容层次 Subsumptive containment hierarchy=====

A ''[[Category theory|subsumptive]]'' containment hierarchy is a classification of object classes from the general to the specific. Other names for this type of hierarchy are "taxonomic hierarchy" and "[[is-a|IS-A]] hierarchy".<ref name="Lehmann"/><ref name="ibm">{{cite web|url=http://publib.boulder.ibm.com/infocenter/wtxdoc/v8r2m0/index.jsp?topic=/com.ibm.websphere.dtx.md.doc/concepts/c_map_design_Compositional_Hierarchy.htm|archive-url=https://archive.today/20130103052727/http://publib.boulder.ibm.com/infocenter/wtxdoc/v8r2m0/index.jsp?topic=/com.ibm.websphere.dtx.md.doc/concepts/c_map_design_Compositional_Hierarchy.htm|url-status=dead|archive-date=3 January 2013|title=Compositional hierarchy|work=WebSphere Transformation Extender Design Studio|accessdate=9 October 2009}}</ref><ref name="sys model">{{cite book|chapter=An advanced modeling environment based on a hybrid AI-OR approach|chapterurl=https://books.google.com/books?id=ds2eIQ6XZy0C&pg=PA366|pages=366–75|last=Funke|first=Birger|last2=Sebastian|first2=Hans-Jürgen|title=Systems modelling and optimization: proceedings of the 18th IFIP TC7 conference|volume=396|series=Research notes in mathematics series|editor1-last=Polis|editor1-first=Michael P.|editor2-last=Dontchev|editor2-first=Asen L.|editor3-last=Kall|editor3-first=Peter|editor4-last=Lascieka|editor4-first=Irena|editor5-last=Olbrot|editor5-first=Andrzej W.|publisher=[[CRC Press]]|year=1999|isbn=978-0-8493-0607-5}}</ref> The last term describes the relationship between each level—a lower-level object "is a" member of the higher class. The taxonomical structure outlined above is a subsumptive containment hierarchy. Using again the example of Linnaean taxonomy, it can be seen that an object that is part of the level ''Mammalia'' "is a" member of the level ''Animalia''; more specifically, a human "is a" primate, a primate "is a" mammal, and so on. A subsumptive hierarchy can also be defined abstractly as a hierarchy of "[[concept]]s".<ref name="sys model"/> For example, with the Linnaean hierarchy outlined above, an entity name like ''Animalia'' is a way to group all the species that fit the [[wikt:conceptualization|conceptualization]] of an animal.

A ''[[Category theory|subsumptive]]'' containment hierarchy is a classification of object classes from the general to the specific. Other names for this type of hierarchy are "taxonomic hierarchy" and "[[is-a|IS-A]] hierarchy".<ref name="Lehmann"/><ref name="ibm">{{cite web|url=http://publib.boulder.ibm.com/infocenter/wtxdoc/v8r2m0/index.jsp?topic=/com.ibm.websphere.dtx.md.doc/concepts/c_map_design_Compositional_Hierarchy.htm|archive-url=https://archive.today/20130103052727/http://publib.boulder.ibm.com/infocenter/wtxdoc/v8r2m0/index.jsp?topic=/com.ibm.websphere.dtx.md.doc/concepts/c_map_design_Compositional_Hierarchy.htm|url-status=dead|archive-date=3 January 2013|title=Compositional hierarchy|work=WebSphere Transformation Extender Design Studio|accessdate=9 October 2009}}</ref><ref name="sys model">{{cite book|chapter=An advanced modeling environment based on a hybrid AI-OR approach|chapterurl=https://books.google.com/books?id=ds2eIQ6XZy0C&pg=PA366|pages=366–75|last=Funke|first=Birger|last2=Sebastian|first2=Hans-Jürgen|title=Systems modelling and optimization: proceedings of the 18th IFIP TC7 conference|volume=396|series=Research notes in mathematics series|editor1-last=Polis|editor1-first=Michael P.|editor2-last=Dontchev|editor2-first=Asen L.|editor3-last=Kall|editor3-first=Peter|editor4-last=Lascieka|editor4-first=Irena|editor5-last=Olbrot|editor5-first=Andrzej W.|publisher=[[CRC Press]]|year=1999|isbn=978-0-8493-0607-5}}</ref> The last term describes the relationship between each level—a lower-level object "is a" member of the higher class. The taxonomical structure outlined above is a subsumptive containment hierarchy. Using again the example of Linnaean taxonomy, it can be seen that an object that is part of the level ''Mammalia'' "is a" member of the level ''Animalia''; more specifically, a human "is a" primate, a primate "is a" mammal, and so on. A subsumptive hierarchy can also be defined abstractly as a hierarchy of "[[concept]]s".<ref name="sys model"/> For example, with the Linnaean hierarchy outlined above, an entity name like ''Animalia'' is a way to group all the species that fit the [[wikt:conceptualization|conceptualization]] of an animal.

<font color="#32CD32">包容层次结构 subsumptive containment hierarchy</font>是对象类从一般到特定的分类。这类层次结构的其他名称是“分类层次结构”和“ IS-A 层次结构”。最后一个术语描述了每个级别之间的关系——较低级别的对象“是”较高级别类的成员。上面概述的分类结构是一个包容性的层次结构。再次使用林奈分类系统的例子，可以看到，属于<font color="#ff8000">哺乳动物 Mammalia </font>等级的物体“是”动物等级的成员；更具体地说，人类“是”灵长类动物，灵长类动物“是”哺乳动物等等。也可以抽象地将包含的层次结构定义为“概念”的层次结构。例如，根据上述的林奈分类系统，像动物这样的实体名称是对所有符合动物概念的物种进行分类的一种方法。

<font color="#32CD32">包容层次结构 subsumptive containment hierarchy</font>是对象类从一般到特定的分类。这类层次结构的其他名称是“分类层次结构”和“ IS-A 层次结构”。最后一个术语描述了每个级别之间的关系——较低级别的对象“是”较高级别类的成员。上面概述的分类结构是一个包容性的层次结构。再次使用林奈分类系统的例子，可以看到，属于<font color="#ff8000">哺乳动物 Mammalia </font>等级的物体“是”动物等级的成员；更具体地说，人类“是”灵长类动物，灵长类动物“是”哺乳动物等等。也可以抽象地将包含的层次结构定义为“概念”的层次结构。例如，根据上述的林奈分类系统，像动物这样的实体名称是对所有符合动物概念的物种进行分类的一种方法。

=====Compositional containment hierarchy=====

=====结构包容层次 Compositional containment hierarchy=====

A ''compositional'' containment hierarchy is an ordering of the parts that make up a system—the system is "composed" of these parts.<ref name="Parsons">{{cite book|last=Parsons|first=David|title=Object Oriented Programming in C++|publisher=Cengage Learning|year=2002|pages=110–185|isbn=0-8264-5428-3}}</ref> Most engineered structures, whether natural or artificial, can be broken down in this manner.

A ''compositional'' containment hierarchy is an ordering of the parts that make up a system—the system is "composed" of these parts.<ref name="Parsons">{{cite book|last=Parsons|first=David|title=Object Oriented Programming in C++|publisher=Cengage Learning|year=2002|pages=110–185|isbn=0-8264-5428-3}}</ref> Most engineered structures, whether natural or artificial, can be broken down in this manner.

在这个特定的例子中，还有一些<font color="#ff8000">涌现特性 emergent properties</font>——在较低层次上看不到的功能（例如<font color="#ff8000">认知 cognition</font>不是神经元的特性，而是大脑的特性）——以及标度特性（分子比原子大，细胞比分子大等等）。这两个概念通常都存在于组合层次结构中，但它们不是必要的一般属性。这些层次结构是拥有属性的双向因果关系。涉及较低层次实体的<font color="#ff8000">上向因果关系  Upward causation</font>导致较高层次实体的某些属性；子实体可以相互作用产生父实体，并且父实体至少部分由他们的子实体组成。<font color="#ff8000">下向因果关系 Downward causation</font>是指将实体 x 并入更高级别的实体可能对 x 的属性和相互作用产生的影响。此外，每个级别上的实体都是<font color="#ff8000">自治的 autonomous</font>。

在这个特定的例子中，还有一些<font color="#ff8000">涌现特性 emergent properties</font>——在较低层次上看不到的功能（例如<font color="#ff8000">认知 cognition</font>不是神经元的特性，而是大脑的特性）——以及标度特性（分子比原子大，细胞比分子大等等）。这两个概念通常都存在于组合层次结构中，但它们不是必要的一般属性。这些层次结构是拥有属性的双向因果关系。涉及较低层次实体的<font color="#ff8000">上向因果关系  Upward causation</font>导致较高层次实体的某些属性；子实体可以相互作用产生父实体，并且父实体至少部分由他们的子实体组成。<font color="#ff8000">下向因果关系 Downward causation</font>是指将实体 x 并入更高级别的实体可能对 x 的属性和相互作用产生的影响。此外，每个级别上的实体都是<font color="#ff8000">自治的 autonomous</font>。

==Contexts and applications==<!--if you change this section's title, please also change the wikilinks throughout the article that link to it! -->

==语境与应用 Contexts and applications==<!--if you change this section's title, please also change the wikilinks throughout the article that link to it! -->

==Contexts and applications 语境和应用==<!--if you change this section's title, please also change the wikilinks throughout the article that link to it! -->

==Contexts and applications 语境和应用==<!--if you change this section's title, please also change the wikilinks throughout the article that link to it! -->